Adding, subtracting, multiplying and dividing can be applied to mixed number fractions. Each has its own method that helps make sure the numerator and denominator are treated correctly.
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Watch this video to learn about dividing fractions.
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For dividing fractions, keep the first fraction as it is, change the divide sign to a multiply and flip the second fraction upside down.
One way to remember this is:
Keep it, change it, flip it
Calculate: \(\frac{3}{8} \div \frac{3}{4}\)
\(= \frac{3}{8} \times \frac{4}{3}\)
Now we use the same method as multiplying fractions:
\(= \frac{{3 \times 4}}{{8 \times 3}}\)
Remember to look out for common factors that can cancel 鈥 in this case we would divide top and bottom by 3 and 4.
\(= \frac{{1 \times 1}}{{2 \times 1}}\)
(if we hadn鈥檛 cancelled we would now have \(\frac{12}{24}\) at this stage)
\(= \frac{1}{2}\)
Now try the example question below.
Calculate: \(5\frac{1}{4} \div 1\frac{2}{5}\)
When dividing mixed numbers change into improper fractions first
\(= \frac{{21}}{4} \div \frac{7}{5}\)
\(= \frac{{21}}{4} \times \frac{5}{7}\)
Cancel the 21 and 7 by dividing them both by 7
\(= \frac{{3 \times 5}}{{4 \times 1}}\)
Multiply the numerators and multiply the denominators
\(= \frac{{15}}{4}\)
Change back into a mixed number
\(= 3\frac{3}{4}\)